Ellipse
(the database of solved problems)
All the problems and solutions shown below were generated using the Ellipse Calculator.
| ID |
Problem |
Count |
| 1301 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 36 } + \dfrac{ \left( y + 4 \right)^2}{ 64 } = 1 $$ | 1 |
| 1302 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 4 } + \dfrac{ \left( y + 6 \right)^2}{ 36 } = 1 $$ | 1 |
| 1303 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 16x^2 + y^2 = 64 $$ | 1 |
| 1304 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 25 } + \dfrac{ \left( y + 1 \right)^2}{ 1 } = 1 $$ | 1 |
| 1305 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 3 \right)^2}{ \sqrt{ 10 } } + \dfrac{ y^2}{ 24 } = 1 $$ | 1 |
| 1306 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 25 } + \dfrac{ y^2}{ 9 } = 1 $$ | 1 |
| 1307 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 1 } + \dfrac{ y^2}{ 16 } = 1 $$ | 1 |
| 1308 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 1 } + \dfrac{ y^2}{ 9 } = 1 $$ | 1 |
| 1309 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 16 } + \dfrac{ y^2}{ 25 } = 1 $$ | 1 |
| 1310 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 49 } + \dfrac{ y^2}{ 16 } = 1 $$ | 1 |
| 1311 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ 49 } = 1 $$ | 1 |
| 1312 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 30 } + \dfrac{ y^2}{ 40 } = 1 $$ | 1 |
| 1313 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 100 } + \dfrac{ y^2}{ 144 } = 1 $$ | 1 |
| 1314 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 144 } + \dfrac{ y^2}{ 100 } = 1 $$ | 1 |
| 1315 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 263 } + \dfrac{ y^2}{ 100 } = 1 $$ | 1 |
| 1316 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 625 } + \dfrac{ y^2}{ 100 } = 1 $$ | 1 |
| 1317 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 75 } + \dfrac{ y^2}{ 43 } = 1 $$ | 1 |
| 1318 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 15 } + \dfrac{ y^2}{ 13 } = 1 $$ | 1 |
| 1319 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 30 } + \dfrac{ y^2}{ 56 } = 1 $$ | 1 |
| 1320 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 7 \right)^2}{ 11 } + \dfrac{ \left( y - 3 \right)^2}{ 36 } = 1 $$ | 1 |
| 1321 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 2 } + \dfrac{ \left( y + 3 \right)^2}{ 3 } = 1 $$ | 1 |
| 1322 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 81 } + \dfrac{ y^2}{ \frac{ 11025 }{ 4 } } = 1 $$ | 1 |
| 1323 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 225 } + \dfrac{ y^2}{ \frac{ 10599 }{ 5 } } = 1 $$ | 1 |
| 1324 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ y^2}{ \frac{ 9 }{ 4 } } = 1 $$ | 1 |
| 1325 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \frac{ 285 }{ 4 }x^2 + 24y^2 = 1 $$ | 1 |
| 1326 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 36 } + \dfrac{ y^2}{ 324 } = 1 $$ | 1 |
| 1327 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 9 } + \dfrac{ \left( y - 7 \right)^2}{ 3 } = 1 $$ | 1 |
| 1328 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 25 } + \dfrac{ y^2}{ 5 } = 1 $$ | 1 |
| 1329 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 100 } + \dfrac{ y^2}{ \frac{ 175 }{ 4 } } = 1 $$ | 1 |
| 1330 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 49 } + \dfrac{ y^2}{ 64 } = 1 $$ | 1 |
| 1331 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 81 } + \dfrac{ \left( y + 9 \right)^2}{ 4 } = 1 $$ | 1 |
| 1332 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 25 } + \dfrac{ \left( y - 1 \right)^2}{ 9 } = 1 $$ | 1 |
| 1333 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 4 \right)^2}{ 16 } + \dfrac{ \left( y - 1 \right)^2}{ 25 } = 1 $$ | 1 |
| 1334 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 1 } + \dfrac{ \left( y - 4 \right)^2}{ \frac{ 1 }{ 4 } } = 1 $$ | 1 |
| 1335 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 49x^2 + 4y^2 = 196 $$ | 1 |
| 1336 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ 18.3062 } + \dfrac{ y^2}{ \frac{ 9061 }{ 1000 } } = 1 $$ | 1 |
| 1337 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \frac{ 181 }{ 10 }x^2 + \frac{ 91 }{ 10 }y^2 = 1 $$ | 1 |
| 1338 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \frac{ 181 }{ 10 } \left( x + \frac{ 91 }{ 10 } \right)^2}{ 1 } + \dfrac{ \frac{ 91 }{ 10 } \left( y + \frac{ 181 }{ 10 } \right)^2}{ 1 } = 1 $$ | 1 |
| 1339 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 181 }{ 10 } } + \dfrac{ y^2}{ \frac{ 91 }{ 10 } } = 1 $$ | 1 |
| 1340 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ 4x^2 + 16y^2 = 340 $$ | 1 |
| 1341 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 1 \right)^2}{ 2 } + \dfrac{ 2 \left( y - 1 \right)^2}{ 1 } = 1 $$ | 1 |
| 1342 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 8 \right)^2}{ 4 } + \dfrac{ \left( y - 3 \right)^2}{ 20 } = 1 $$ | 1 |
| 1343 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 2 \right)^2}{ 4 } + \dfrac{ \left( y - 2 \right)^2}{ 9 } = 1 $$ | 1 |
| 1344 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x - 4 \right)^2}{ 16 } + \dfrac{ \left( y + 3 \right)^2}{ 9 } = 1 $$ | 1 |
| 1345 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ \left( x + 2 \right)^2}{ 4 } + \dfrac{ \left( y - 3 \right)^2}{ 25 } = 1 $$ | 1 |
| 1346 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 4 }{ 5 } } + \dfrac{ \left( y - \frac{ 5 }{ 2 } \right)^2}{ \frac{ 3 }{ 5 } } = 1 $$ | 1 |
| 1347 | Find foci, vertices, lengths of major and minor axes and the eccentricity of the ellipse:$$ \dfrac{ x^2}{ \frac{ 1 }{ 10 } } + \dfrac{ \left( y - \frac{ 5 }{ 2 } \right)^2}{ \frac{ 2 }{ 25 } } = 1 $$ | 1 |
